Scalor product/vectors?

Using the definition of the scalar product, find the angles between the following pairs of vectors.


(a) A = - 3 i + j k and B = 2 i j - 3k








(b) = 2i - 3 j k and = - 2i - j - k








(c) = - 4i + 5 j k and = 3i + 4j - k

Scalor product/vectors?
One problem per question please.





The dot or scalar product for vectors u and v can be defined as:





u • v = || u || || v || cosθ


where θ is the angle between the two vectors





cosθ = (u • v) / (|| u || || v ||)


_______________





I assume you mean:





(a) A = - 3i + j + k and B = 2i + j - 3k





A = %26lt;-3, 1, 1%26gt; and B = %26lt;2, 1, -3%26gt;





A • B = %26lt;-3, 1, 1%26gt; • %26lt;2, 1, -3%26gt; = -3*2 + 1*1 + 1*(-3) = -8





|| A || = √[(-3)² + 1² + 1²) = √(9 + 1 + 1) = √11


|| B || = √[2² + 1² + (-3)²] = √(4 + 1 + 9) = √14





Now plug into the formula for cosθ.





cosθ = (u • v) / (|| u || || v ||)


cosθ = -8 / (√11 * √14) = -8/√154





θ = arccos(-8/√154) ≈ 130.14007°